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Detection and evaluation of clusters within sequential data. [PDF]

Data Min Knowl Discov
Van Werde A, Senen-Cerda A, Kosmella G, Sanders J.   +3 more
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Singular singular-perturbation problems

1977
Abstract : Consider initial problems for nonlinear singularly perturbed systems of the form epsilon sub z dot = f(z,t,epsilon) in the singular situation that f sub z(z,t,0) has a nontrivial null space. Under appropriate hypotheses, such problems have asymptotic solutions as epsilon approaches 0 for t or = 0 consisting of the sum of a function of t and ...
R. E. O'Malley, J. E. Flaherty
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Singular Perturbation Problems

2004
In this chapter the problems when the small parameter stands by a highest order derivatives are considered. Note that for e = 0 a qualitative change of the system occurs since the system order of the analysed differential equation is decreased. The similar like asymptotics is called the singular one.
I. Andrianov, J. Awrejcewicz, L. I. Manevitch   +2 more
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Homogenization of a Singular Perturbation Problem

Journal of Mathematical Sciences, 2019
The authors investigate the passage to the homogenization limit done simultaneously with the passage to the limit in yet another independent parameter. Under suitable assumptions and choices of the ordering between the two small parameters, the authors are able to show that there is a case when the limit (weak) solution satisfies a standard Bernoulli ...
Kim, S., Shahgholian, H.
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Asymptotically Equivalent Singular Perturbation Problems

Studies in Applied Mathematics, 1976
A study is made of a two‐point nonlinear boundary‐value problem with a small parameter multiplying the highest derivative. It is shown that under certain circumstances the asymptotic solution to the problem is expressible in terms of the solution to a linear boundary‐value problem—in which case the two problems are said to be asymptotically equivalent.
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Quadratic Singular Perturbation Problems

1984
In this chapter we investigate the asymptotic behavior of solutions of boundary value problems for the differential equation $$\varepsilon y''{\text{ = p}}\left( {{\text{t}},{\text{y}}} \right){{\text{y'}}^{\text{2}}}{\text{ + g}}\left( {{\text{t}},{\text{y}}} \right),{\text{a}} < {\text{t}} < {\text{b}}$$ (DE) The novelty here is the ...
K. W. Chang, F. A. Howes
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Singular Perturbation Problems

1951
The equations considered in this rarer are linear differential equations in one and two independent variables. The problem at hand is to study solutions of boundary value problems for these equations in their dependence on a small parameter ϵ. Specifically, the equations are of the form (A) ϵ Nɸ + Mɸ = 0 where M, N are linear differential expressions,
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Quasilinear Singular Perturbation Problems

1984
We consider now the singularly perturbed quasilinear Dirichlet problem $$\begin{gathered} \varepsilon y''{\text{ }} = {\text{ f}}({\text{t}},y)y'{\text{ }} + {\text{ g(t}},y{\text{) }} \equiv {\text{ F}}({\text{t}},y,y'),{\text{ a }} < {\text{ t }} < {\text{ b}}, \hfill \\ y({\text{a}},\varepsilon ){\text{ }} = {\text{A}},{\text{ }}y({\text{b ...
K. W. Chang, F. A. Howes
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Superquadratic Singular Perturbation Problems

1984
In previous chapters we have presented fairly comprehensive results for boundary value problems involving the differential equation $$\varepsilon y''{\text{ = f}}\left( {t,y,y'} \right),{\text{a}} < {\text{t}} < {\text{b}}$$ subject to the fundamental restriction: $$f(t.y,z) = 0({\left| z \right|^2})as\left| z \right| \to \infty .$$
K. W. Chang, F. A. Howes
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Singular Perturbation Problems

1985
An operator L = L(e) depending on a parameter e is called singularly perturbed if the limiting operator \(L(0) = \begin{array}{*{20}{c}} {\lim } \\ {\varepsilon \to 0} \end{array}L(\varepsilon )\) is of a type other than L(e) for e > 0. For instance, an elliptic operator L(e) = e L I + L II (e > 0) is singularly perturbed if L II is non-elliptic or ...
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